{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T13:14:21Z","timestamp":1695302061540},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,6,22]],"date-time":"2012-06-22T00:00:00Z","timestamp":1340323200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2012,10]]},"DOI":"10.1007\/s11075-012-9607-5","type":"journal-article","created":{"date-parts":[[2012,6,21]],"date-time":"2012-06-21T16:05:46Z","timestamp":1340294746000},"page":"261-274","source":"Crossref","is-referenced-by-count":3,"title":["Error analysis of the mdLVs algorithm for computing bidiagonal singular values"],"prefix":"10.1007","volume":"61","author":[{"given":"Munehiro","family":"Nagata","sequence":"first","affiliation":[]},{"given":"Masashi","family":"Iwasaki","sequence":"additional","affiliation":[]},{"given":"Yoshimasa","family":"Nakamura","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,6,22]]},"reference":[{"key":"9607_CR1","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.laa.2004.02.004","volume":"384","author":"MI Bueno","year":"2004","unstructured":"Bueno, M.I., Marcellan, F.: Darboux transformation and perturbation of linear functionals. Linear Algebra Appl. 384, 215\u2013242 (2004)","journal-title":"Linear Algebra Appl."},{"key":"9607_CR2","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.cam.2006.05.027","volume":"205","author":"MI Bueno","year":"2007","unstructured":"Bueno, M.I., Dopico, F.M.: A more accurate algorithm for computing the Christoffel transformation. J. Comput. Appl. Math. 205, 567\u2013582 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"9607_CR3","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719673","volume-title":"Lectures on Finite Precision Computations","author":"F Chaitin-Chatelin","year":"1996","unstructured":"Chaitin-Chatelin, F., Fraysse, V.: Lectures on Finite Precision Computations. SIAM, Philadelphia (1996)"},{"key":"9607_CR4","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1137\/0911052","volume":"11","author":"J Demmel","year":"1990","unstructured":"Demmel, J., Kahan, W.: Accurate singular values of bidiagonal matrices. SIAM J. Sci. Statist. Comput. 11, 873\u2013912 (1990)","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"9607_CR5","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s002110050024","volume":"67","author":"KV Fernando","year":"1994","unstructured":"Fernando, K.V., Parlett, B.N.: Accurate singular values and differential qd algorithms. Numer. Math. 67, 191\u2013229 (1994)","journal-title":"Numer. Math."},{"key":"9607_CR6","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718027","volume-title":"Accuracy and Stability of Numerical Algorithms","author":"NJ Higham","year":"2002","unstructured":"Higham, N.J.: Accuracy and Stability of Numerical Algorithms, 2nd edn. SIAM, Philadelphia (2002)","edition":"2"},{"key":"9607_CR7","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1143\/JPSJ.66.283","volume":"66","author":"R Hirota","year":"1997","unstructured":"Hirota, R.: Conserved quantities of a random-time Toda equation. J. Phys. Soc. Jpn. 66, 283\u2013284 (1997)","journal-title":"J. Phys. Soc. Jpn."},{"key":"9607_CR8","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1088\/0266-5611\/18\/6\/309","volume":"18","author":"M Iwasaki","year":"2002","unstructured":"Iwasaki, M., Nakamura, Y.: On the convergence of a solution of the discrete Lotka\u2013Volterra system. Inverse Probl. 18, 1569\u20131578 (2002)","journal-title":"Inverse Probl."},{"key":"9607_CR9","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1088\/0266-5611\/20\/2\/015","volume":"20","author":"M Iwasaki","year":"2004","unstructured":"Iwasaki, M., Nakamura, Y.: An application of the discrete Lotka\u2013Volterra system with variable step-size to singular value computation. Inverse Probl. 20, 553\u2013563 (2004)","journal-title":"Inverse Probl."},{"key":"9607_CR10","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/BF03167593","volume":"23","author":"M Iwasaki","year":"2006","unstructured":"Iwasaki, M., Nakamura, Y.: Accurate computation of singular values in terms of shifted integrable schemes. Jpn. J. Ind. Appl. Math. 23, 239\u2013259 (2006)","journal-title":"Jpn. J. Ind. Appl. Math."},{"key":"9607_CR11","first-page":"184","volume":"38","author":"M Iwasaki","year":"2011","unstructured":"Iwasaki, M., Nakamura, Y.: Positivity of dLV and mdLVs algorithms for computing singular values. Elec. Trans. Numer. Anal. 38, 184\u2013201 (2011)","journal-title":"Elec. Trans. Numer. Anal."},{"key":"9607_CR12","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1017\/S0962492900002580","volume":"4","author":"BN Parlett","year":"1995","unstructured":"Parlett, B.N.: The new qd algorithm. Acta Numer. 4, 459\u2013491 (1995)","journal-title":"Acta Numer."},{"key":"9607_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3468-5","volume-title":"Lectures on Numerical Mathematics","author":"H Rutishauser","year":"1990","unstructured":"Rutishauser, H.: Lectures on Numerical Mathematics. Brinkh\u00e4user, Boston (1990)"},{"key":"9607_CR14","doi-asserted-by":"crossref","first-page":"8727","DOI":"10.1088\/0305-4470\/30\/24\/031","volume":"30","author":"V Spiridonov","year":"1997","unstructured":"Spiridonov, V., Zhedanov, A.: Discrete-time Volterra chain and classical orthogonal polynomials. J. Phys. A.: Math. Gen. 30, 8727\u201337 (1997)","journal-title":"J. Phys. A.: Math. Gen."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9607-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-012-9607-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9607-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T01:08:18Z","timestamp":1559351298000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-012-9607-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,22]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,10]]}},"alternative-id":["9607"],"URL":"https:\/\/doi.org\/10.1007\/s11075-012-9607-5","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,22]]}}}